Monte Carlo Simulations of the Photospheric Process

We present a Monte Carlo (MC) code we wrote to simulate the photospheric process and to study the photospheric spectrum above the peak energy. Our simulations were performed with a photon to electron ratio $N_{\gamma}/N_{e} = 10^{5}$, as determined by observations of the GRB prompt emission. We searched an exhaustive parameter space to determine if the photospheric process can match the observed high-energy spectrum of the prompt emission. If we do not consider electron re-heating, we determined that the best conditions to produce the observed high-energy spectrum are low photon temperatures and high optical depths. However, for these simulations, the spectrum peaks at an energy below 300 keV by a factor $\sim 10$. For the cases we consider with higher photon temperatures and lower optical depths, we demonstrate that additional energy in the electrons is required to produce a power-law spectrum above the peak-energy. By considering electron re-heating near the photosphere, the spectrum for these simulations have a peak-energy $\sim \mbox{300 keV}$ and a power-law spectrum extending to at least 10 MeV with a spectral index consistent with the prompt emission observations. We also performed simulations for different values of $N_{\gamma}/N_{e}$ and determined that the simulation results are very sensitive to $N_{\gamma}/N_{e}$. Lastly, in addition to Comptonizing a Blackbody spectrum, we also simulate the Comptonization of a $f_{\nu} \propto \nu^{-1/2}$ fast cooled synchrotron spectrum. The spectrum for these simulations peaks at $\sim 10^{4} \mbox{ keV}$, with a flat spectrum $f_{\nu} \propto \nu^{0}$ below the peak energy.